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Simplifying 2x2 + 14x + 24 = 220 Reorder the terms: 24 + 14x + 2x2 = 220 Solving 24 + 14x + 2x2 = 220 Solving for variable 'x'. Reorder the terms: 24 + -220 + 14x + 2x2 = 220 + -220 Combine like terms: 24 + -220 = -196 -196 + 14x + 2x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -196 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-98 + 7x + x2) = 0 Factor a trinomial. 2((-14 + -1x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-14, 7}
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